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2 days ago vote accept user467048
2 days ago comment added Michael Seifert @user467048: The fact that the field lines are not parallel to the axis turns out to make a difference. To see this, imagine a tiny cylinder rather than a sphere. The flux into the cylinder through the "near" end cap is greater than the flux out of the "far" end cap, because of the reasons you've outlined. But because the B-field isn't parallel to the axis, there's also a small amount of flux out through the curved side wall of the cylinder. This small amount of outward flux exactly compensates for the difference in the fluxes between the end caps, and makes it so that the net flux is zero.
2 days ago comment added user467048 Badly hand drawn ms paint diagram for reference: link
2 days ago comment added user467048 Thank you for your reply, you really did shed light on some aspects of the subject that I didn't grasp quite firmly before. This question started from a thought experiment I imagined based on the behaviour of the magnetic field along the axis of a solenoid coil, but outside of the solenoid's length. There I assumed the field to be more or less parallel to the axis, but to get weaker with the distance from the solenoid (which i called z in my original question). Would such a configuration be possible and follow something akin to what I described in the question?
2 days ago history answered Michael Seifert CC BY-SA 4.0